Subshifts defined by nondeterministic and alternating plane-walking automata
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917924094083072 |
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| author | de Menibus, Benjamin Hellouin Perrotin, Pacôme |
| author_facet | de Menibus, Benjamin Hellouin Perrotin, Pacôme |
| contents | Plane-walking automata were introduced by Salo & Törma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of $4$-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic subshifts, and that the classes corresponding to existential and universal nondeterminism are incomparable and both larger that the deterministic class. We define a hierarchy of subshifts recognised by plane-walking automata with alternating quantifiers, which we conjecture to be strict. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08024 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subshifts defined by nondeterministic and alternating plane-walking automata de Menibus, Benjamin Hellouin Perrotin, Pacôme Formal Languages and Automata Theory 68Q45, 37B51, 68Q10 F.4.3; F.1.2 Plane-walking automata were introduced by Salo & Törma to recognise languages of two-dimensional infinite words (subshifts), the counterpart of $4$-way finite automata for two-dimensional finite words. We extend the model to allow for nondeterminism and alternation of quantifiers. We prove that the recognised subshifts form a strict subclass of sofic subshifts, and that the classes corresponding to existential and universal nondeterminism are incomparable and both larger that the deterministic class. We define a hierarchy of subshifts recognised by plane-walking automata with alternating quantifiers, which we conjecture to be strict. |
| title | Subshifts defined by nondeterministic and alternating plane-walking automata |
| topic | Formal Languages and Automata Theory 68Q45, 37B51, 68Q10 F.4.3; F.1.2 |
| url | https://arxiv.org/abs/2409.08024 |